Foreigners tend to jump to conclusions and are quick to say that whenever something does not please them about Korean people, it's because Korean people are racist.
Before we start asking the question of what is racism in Korea, we should ask ourselves the question of who is racist in Korea: the Korean who refuses to sit next to a foreigner, who openly states that he dislikes foreigners, laws that prohibit foreigners from buying cell phones and limit their right to having health care?
Or the foreigner who calls Koreans "stupid", "insular", "sectarian", who claims that they are incapable of learning English, that they are "weird" people who don't fit in the global community etc. etc.?
Defining racism without judging a person is a hard thing to do. But let's try to do that. Most societies in the world have a story, a legend or a book that claims directly or indirectly that their way of life is the best. With the advent of science and technology, there was even an attempt by white people to define themselves as scientifically superior to all other people. Until as late as the 1950s, many scientists considered valid the theory according the which white men had evolved from black and Asian men and that they represented humanity in its perfect state. Even in recent years, scientists have tried to demonstrate that AIDS was related to race in some way, that black people were predisposed to getting AIDS and that Asians were not. Other theories have suggested that black people were biologically more fit for activities like sports and dancing and that white people were biologically more fit for intellectual activities. These theories still have not been discarded, although there is very strong scientific evidence contradicting these facts.
Geneticists and biologists have demonstrated that in fact black populations and Asian populations had as much variation as their genes as any other people and that genetically there is no such thing as "white people", "black people" or "Asian people". Calling someone a "white" person has social implications in the sense that it does define his identity, but very little genetic implications as he may be genetically very different from any other white person.
What does this mean for Korea? Over the past 4 centuries white people have tried every method to prove that they were superior people. White people stopped using the term superior or explicitly claiming that they were better than other peoples after the Holocaust, but Korea is one of those countries where it can clearly be seen that white people do have this heritage of thinking of itself as a "superior" race.
If not, why is it then that foreigners criticize everything in Korea from food to people ("Koreans lack self-confidence", "Koreans don't want to mix with foreigners", "Koreans are too stupid to learn English"), to the culture ("Koreans have a hierarchical society which is bad", "Korean workers kiss their boss's behinds", "Koreans are hypocrites and will never say the truth to your face"). From what perspective are all the things that I just described "bad"? Certainly not from a Korean perspective... Just like every society on earth, people tend to think that their way of doing things is the "best" way. More so that for centuries now the white race has been trying to prove that it is a superior race, and that therefore its way of life is superior to other people's way of life, and that with globalization some non-white people have actually bought this theory and started questioning themselves.
As for Koreans, there have been some verbal assaults on foreigners reported (marginal ones) and I've never heard about a physical assault on a foreigner. Here's a Q and A session on the reasons Koreans behave in what some call a "racist" way:
Why aren't foreigners allowed to buy cell phones?:
As I have said many times, Koreans place huge importance on trust. They feel that they can not trust someone who will buy a cell phone and who may leave the country without paying his phone bills. Koreans want to identify people who use cell phones through a very strict identification system because of a security law since the country is technically at war. Since foreigners' identification usually expires within a year, and that contracts tend to last for at least a year, they do not allow foreigners to buy cell phones.
Why can't foreign students get health care?:
Koreans consider a wife or a boss at a company to be legal sponsors, but not universities. The health care system requires that foreigners get a sponsor, be affiliated with an organization to get health care. Because universities are large crowded areas where people have relative freedom and no official sponsor, Korean authorities don't consider universities as organizations. Health care is partly covered by the Korean government, partly by companies, but is not covered by universities. And foreign students do not pay taxes and do not have parents who pay taxes in Korea, and it is therefore considered that the government should not pay for things that citizens do not pay taxes for in return.
Why do Koreans refuse to sit next to foreigners in buses or subways?:
There is an etiquette for who to sit next to in buses or subways in Korea. People should choose to sit to the person who resembles them the most. Young men will chose to sit in priority next to young men, then old men, then old women, then young women. Old women will choose to sit next to old women, young women, young men, old women. Foreigners are considered not to fit in the "identity criteria" and are placed last in the list, because they resemble Koreans the least. That is because while Koreans can act in predictable ways, foreigners act in unpredictable ways.
Why do Koreans use 반말 when they speak to foreigners?
Any older person can use 반말 with a person who is visibly younger or the same age, and the same is done with Koreans. Though it is not the "recommended" thing to do, many do not follow the rule.
Other questions, including why Koreans don't hire non-white people for English teaching jobs, why Koreans grab and push foreigners rather than talk to them, etc. have been answered in this blog.
The point is that while some Koreans may claim to dislike foreigners, it may not compare with how much foreigners claim to dislike Koreans.